Abstract: It is shown that the Gromov translation ring of a discrete tree over a von Neumann regular ring is an exchange ring. This provides a new source of exchange rings, including, for example, the algebras of matrices (over a field) of constant bandwidth. An extension of these ideas shows that for all real numbers in the unit interval , the growth algebras (introduced by Hannah and O'Meara in 1993) are exchange rings. Consequently, over a countable field, countable-dimensional exchange algebras can take any prescribed bandwidth dimension in .

K. C. O'MearaAffiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand
Address at time of publication:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email:
K.OMeara@math.canterbury.ac.nz, staf198@ext.canterbury.ac.nz